Inflation may be occurring domestically in the US but the rest of the world is demanding dollars as well, offsetting the money supply increase by a significant margin. This is when the interest rates will start to rise in an attempt to slow demand, since the unlikely alternative of simply introducing more dollars at a pace sufficient to handle the demand has become politically unpalatable.
I believe what you are saying is by raising interest rates on bonds, then demand for bonds can be reduced because investors will anticipate further interest rates hikes thus devaluing the already issued bonds at lower interest rates. Thus discouraging capital to convert FOREX to buy dollar bonds.
And this selloff of bonds will ignite a frenzy of buying in the stock market.